Chapter 23b - Chapter 23: Gauss Law Part B Applications of...

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September 9, 2009 Ch. 23: Gauss' Law - Part B 1 Chapter 23: Gauss’ Law – Part B Applications of Gauss’ Law ! Cylindrical symmetry. ! A charged isolated conductor. ! Electric field inside a conductor. ! Electric field outside the conductor. ! A point charge inside a conducting shell. ! HITT question. ! A charged nonconducting sheet.
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September 9, 2009 Ch. 23: Gauss' Law - Part B 2 Gaussian Surface ! A hypothetical (imaginary) closed surface that encloses the charge distribution. ! Any shape, but should mimic the symmetry of the charge distribution in order to minimize the electric field calculations. Gaussian surface Gaussian surface
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September 9, 2009 Ch. 23: Gauss' Law - Part B 3 Gauss’ Law ! The electric field through any closed surface is proportional to the enclosed electric charge. ! Gauss’ law for vacuum (or air) medium: 0 0 ε ⋅= Φ= !! " enc enc q Ed A q ! The enclosed charge is the algebraic sum of all the enclosed positive and negative charges. It could be positive, negative or zero. ! If q enc is positive, the flux is outward, if q enc is negative, the flux is inward.
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September 9, 2009 Ch. 23: Gauss' Law - Part B 4 Applying Gauss’ Law ! Cylindrical symmetry ! Infinitely long cylindrical plastic rod. ! Uniform positive charge density λ . ! Find the magnitude of the electric field at a distance r from the axis of the rod. ! Choose a cylindrical Gaussian surface, coaxial with the rod; ! Circular cylinder, radius r, length h. ! The electric field is perpendicular to the cylinder surface, pointing radially outward (+q). ! There is no flux through the end caps (E is parallel to these surface).
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September 9, 2009 Ch. 23: Gauss' Law - Part B 5 Applying Gauss’ Law ! Cylindrical symmetry 0 2 E r λ πε = 0 0 20 2 2 cos () c o s , enc enc E d AE A Er h h qq h h h θ ππ ελ επ ⋅= = = == = Φ= Φ !
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Chapter 23b - Chapter 23: Gauss Law Part B Applications of...

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